# How do you simplify and find the excluded value of (3z^2 + z) /( 18z + 6 )?

May 4, 2018

$\text{see explanation}$

#### Explanation:

$\text{the excluded values are any values of z that make the}$
$\text{denominator equal zero as this would make the rational}$
$\text{function undefined. Equating the denominator to zero}$
$\text{and solving gives the value that z cannot be}$

$\text{solve } 18 z + 6 = 0 \Rightarrow 18 z = - 6 \Rightarrow z = - \frac{6}{18} = - \frac{1}{3}$

$\Rightarrow z = - \frac{1}{3} \leftarrow \textcolor{red}{\text{is the excluded value}}$

$\text{To simplify factor numerator/denominator and cancel}$
$\text{any common factors}$

$\Rightarrow \frac{z \cancel{\left(3 z + 1\right)}}{6 \cancel{\left(3 z + 1\right)}} = \frac{z}{6}$